Simplify the following expression: $y = \dfrac{a^2 - 4a - 45}{a + 5} $
First factor the polynomial in the numerator. $ a^2 - 4a - 45 = (a + 5)(a - 9) $ So we can rewrite the expression as: $y = \dfrac{(a + 5)(a - 9)}{a + 5} $ We can divide the numerator and denominator by $(a + 5)$ on condition that $a \neq -5$ Therefore $y = a - 9; a \neq -5$